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Poier PP, Lagardère L, Piquemal JP. Smooth particle mesh Ewald-integrated stochastic Lanczos many-body dispersion algorithm. J Chem Phys 2023; 159:154109. [PMID: 37861116 DOI: 10.1063/5.0166476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 10/02/2023] [Indexed: 10/21/2023] Open
Abstract
We derive and implement an alternative formulation of the Stochastic Lanczos algorithm to be employed in connection with the Many-Body Dispersion model (MBD). Indeed, this formulation, which is only possible due to the Stochastic Lanczos' reliance on matrix-vector products, introduces generalized dipoles and fields. These key quantities allow for a state-of-the-art treatment of periodic boundary conditions via the O(Nlog(N)) Smooth Particle Mesh Ewald (SPME) approach which uses efficient fast Fourier transforms. This SPME-Lanczos algorithm drastically outperforms the standard replica method which is affected by a slow and conditionally convergence rate that limits an efficient and reliable inclusion of long-range periodic boundary conditions interactions in many-body dispersion modelling. The proposed algorithm inherits the embarrassingly parallelism of the original Stochastic Lanczos scheme, thus opening up for a fully converged and efficient periodic boundary conditions treatment of MBD approaches.
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Affiliation(s)
- Pier Paolo Poier
- Laboratoire de Chimie Théorique, Sorbonne Université, 75005 Paris, France
| | - Louis Lagardère
- Laboratoire de Chimie Théorique, Sorbonne Université, 75005 Paris, France
- Sorbonne Université, IP2CT, FR 2622 CNRS, Paris, France
| | - Jean-Philip Piquemal
- Laboratoire de Chimie Théorique, Sorbonne Université, 75005 Paris, France
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA
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2
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Chollet I, Lagardère L, Piquemal JP. ANKH: A Generalized O( N) Interpolated Ewald Strategy for Molecular Dynamics Simulations. J Chem Theory Comput 2023; 19:2887-2905. [PMID: 37134146 DOI: 10.1021/acs.jctc.3c00015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
To evaluate electrostatics interactions, molecular dynamics (MD) simulations rely on Particle Mesh Ewald (PME), an O(Nlog(N)) algorithm that uses Fast Fourier Transforms (FFTs) or, alternatively, on O(N) Fast Multipole Methods (FMM) approaches. However, the FFTs low scalability remains a strong bottleneck for large-scale PME simulations on supercomputers. On the opposite, FFT-free FMM techniques are able to deal efficiently with such systems but they fail to reach PME performances for small- to medium-size systems, limiting their real-life applicability. We propose ANKH, a strategy grounded on interpolated Ewald summations and designed to remain efficient/scalable for any size of systems. The method is generalized for distributed point multipoles, and so for induced dipoles, which makes it suitable for high performance simulations using new generation polarizable force fields toward exascale computing.
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Affiliation(s)
- Igor Chollet
- LAGA, Université Sorbonne Paris Nord, UMR 7539, Villetaneuse, France and LCT, Sorbonne Université, UMR 7616, Paris, 75006, France
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3
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Karjalainen J, Henschel H, Nissi MJ, Nieminen MT, Hanni M. Dipolar Relaxation of Water Protons in the Vicinity of a Collagen-like Peptide. J Phys Chem B 2022; 126:2538-2551. [PMID: 35343227 PMCID: PMC8996236 DOI: 10.1021/acs.jpcb.2c00052] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
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Quantitative magnetic
resonance imaging is one of the few available
methods for noninvasive diagnosis of degenerative changes in articular
cartilage. The clinical use of the imaging data is limited by the
lack of a clear association between structural changes at the molecular
level and the measured magnetic relaxation times. In anisotropic,
collagen-containing tissues, such as articular cartilage, the orientation
dependency of nuclear magnetic relaxation can obscure the content
of the images. Conversely, if the molecular origin of the phenomenon
would be better understood, it would provide opportunities for diagnostics
as well as treatment planning of degenerative changes in these tissues.
We study the magnitude and orientation dependence of the nuclear magnetic
relaxation due to dipole–dipole coupling of water protons in
anisotropic, collagenous structures. The water–collagen interactions
are modeled with molecular dynamics simulations of a small collagen-like
peptide dissolved in water. We find that in the vicinity of the collagen-like
peptide, the dipolar relaxation of water hydrogen nuclei is anisotropic,
which can result in orientation-dependent relaxation times if the
water remains close to the peptide. However, the orientation-dependency
of the relaxation is different from the commonly observed magic-angle
phenomenon in articular cartilage MRI.
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Affiliation(s)
- Jouni Karjalainen
- Research Unit of Medical Imaging Physics and Technology, University of Oulu, P.O. Box 5000, Oulu 90014, Finland
| | - Henning Henschel
- Research Unit of Medical Imaging Physics and Technology, University of Oulu, P.O. Box 5000, Oulu 90014, Finland
| | - Mikko J Nissi
- Research Unit of Medical Imaging Physics and Technology, University of Oulu, P.O. Box 5000, Oulu 90014, Finland.,Department of Applied Physics, University of Eastern Finland, Kuopio 70210, Finland
| | - Miika T Nieminen
- Research Unit of Medical Imaging Physics and Technology, University of Oulu, P.O. Box 5000, Oulu 90014, Finland.,Department of Diagnostic Radiology, Oulu University Hospital, Oulu 90014, Finland.,Medical Research Center, University of Oulu and Oulu University Hospital, Oulu 90014, Finland
| | - Matti Hanni
- Research Unit of Medical Imaging Physics and Technology, University of Oulu, P.O. Box 5000, Oulu 90014, Finland.,Department of Diagnostic Radiology, Oulu University Hospital, Oulu 90014, Finland.,Medical Research Center, University of Oulu and Oulu University Hospital, Oulu 90014, Finland
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4
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Burnham CJ, English NJ. A New Relatively Simple Approach to Multipole Interactions in Either Spherical Harmonics or Cartesians, Suitable for Implementation into Ewald Sums. Int J Mol Sci 2019; 21:ijms21010277. [PMID: 31906127 PMCID: PMC7017380 DOI: 10.3390/ijms21010277] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 12/12/2019] [Accepted: 12/20/2019] [Indexed: 11/16/2022] Open
Abstract
We present a novel derivation of the multipole interaction (energies, forces and fields) in spherical harmonics, which results in an expression that is able to exactly reproduce the results of earlier Cartesian formulations. Our method follows the derivations of Smith (W. Smith, CCP5 Newsletter 1998, 46, 18.) and Lin (D. Lin, J. Chem. Phys. 2015, 143, 114115), who evaluate the Ewald sum for multipoles in Cartesian form, and then shows how the resulting expressions can be converted into spherical harmonics, where the conversion is performed by establishing a relation between an inner product on the space of symmetric traceless Cartesian tensors, and an inner product on the space of harmonic polynomials on the unit sphere. We also introduce a diagrammatic method for keeping track of the terms in the multipole interaction expression, such that the total electrostatic energy can be viewed as a 'sum over diagrams', and where the conversion to spherical harmonics is represented by 'braiding' subsets of Cartesian components together. For multipoles of maximum rank n, our algorithm is found to have scaling of n 3.7 vs. n 4.5 for our most optimised Cartesian implementation.
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Bedrov D, Piquemal JP, Borodin O, MacKerell AD, Roux B, Schröder C. Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields. Chem Rev 2019; 119:7940-7995. [PMID: 31141351 PMCID: PMC6620131 DOI: 10.1021/acs.chemrev.8b00763] [Citation(s) in RCA: 284] [Impact Index Per Article: 56.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 11/30/2022]
Abstract
Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.
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Affiliation(s)
- Dmitry Bedrov
- Department
of Materials Science & Engineering, University of Utah, 122 South Central Campus Drive, Room 304, Salt Lake City, Utah 84112, United States
| | - Jean-Philip Piquemal
- Laboratoire
de Chimie Théorique, Sorbonne Université,
UMR 7616 CNRS, CC137, 4 Place Jussieu, Tour 12-13, 4ème étage, 75252 Paris Cedex 05, France
- Institut
Universitaire de France, 75005, Paris Cedex 05, France
- Department
of Biomedical Engineering, The University
of Texas at Austin, Austin, Texas 78712, United States
| | - Oleg Borodin
- Electrochemistry
Branch, Sensors and Electron Devices Directorate, Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20703, United
States
| | - Alexander D. MacKerell
- Department
of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, Maryland 21201, United
States
| | - Benoît Roux
- Department
of Biochemistry and Molecular Biology, Gordon Center for Integrative
Science, University of Chicago, 929 57th Street, Chicago, Illinois 60637, United States
| | - Christian Schröder
- Department
of Computational Biological Chemistry, University
of Vienna, Währinger Strasse 17, A-1090 Vienna, Austria
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Lagardère L, Aviat F, Piquemal JP. Pushing the Limits of Multiple-Time-Step Strategies for Polarizable Point Dipole Molecular Dynamics. J Phys Chem Lett 2019; 10:2593-2599. [PMID: 31050904 DOI: 10.1021/acs.jpclett.9b00901] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We propose an incremental construction of multi-time-step integrators to accelerate polarizable point dipole molecular dynamics while preserving sampling efficiency. We start by building integrators using frequency-driven splittings of energy terms and a Velocity-Verlet evaluation of the most rapidly varying forces and compare a standard bonded/nonbonded split to a three-group split dividing nonbonded forces (including polarization) into short- and long-range contributions. We then introduce new approaches by coupling these splittings to Langevin dynamics and to Leimkuhler's BAOAB integrator in order to reach larger time steps (6 fs) for long-range forces. We further increase sampling efficiency by (i) accelerating the polarization evaluation using a fast/noniterative truncated conjugate gradient (TCG-1) as a short-range solver and (ii) pushing the outer time step to 10 fs using hydrogen mass repartitioning. The new BAOAB-RESPA1 integrators demonstrate up to a 7-fold acceleration over standard 1 fs (Tinker-HP) integration and reduce the performance gap between polarizable and classical force fields while preserving static and dynamical properties.
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Affiliation(s)
- Louis Lagardère
- Institut Parisien de Chimie Physique et Theorique , Sorbonne Université, FR2622 CNRS , F-75005 Paris , France
- Institut des Sciences du Calcul et des Données , Sorbonne Université , F-75005 Paris , France
| | - Félix Aviat
- Institut des Sciences du Calcul et des Données , Sorbonne Université , F-75005 Paris , France
- Laboratoire de Chimie Théorique , Sorbonne Université, UMR 7616 CNRS , F-75005 Paris , France
| | - Jean-Philip Piquemal
- Laboratoire de Chimie Théorique , Sorbonne Université, UMR 7616 CNRS , F-75005 Paris , France
- Institut Universitaire de France , F-75005 Paris , France
- The University of Texas at Austin, Department of Biomedical Engineering, Texas , United States
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Holden ZC, Rana B, Herbert JM. Analytic gradient for the QM/MM-Ewald method using charges derived from the electrostatic potential: Theory, implementation, and application to ab initio molecular dynamics simulation of the aqueous electron. J Chem Phys 2019; 150:144115. [DOI: 10.1063/1.5089673] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Zachary C. Holden
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Bhaskar Rana
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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